We show that the ratio of galaxies specific star formation rates (SSFRs) to their host halos specific mass accretion rates (SMARs) strongly constrains how the galaxies stellar masses, specific star formation rates, and host halo masses evolve over cosmic time. This evolutionary constraint provides a simple way to probe z>8 galaxy populations without direct observations. Tests of the method with galaxy properties at z=4 successfully reproduce the known evolution of the stellar mass--halo mass (SMHM) relation, galaxy SSFRs, and the cosmic star formation rate (CSFR) for 5<z<8. We then predict the continued evolution of these properties for 8<z<15. In contrast to the non-evolution in the SMHM relation at z<4, the median galaxy mass at fixed halo mass increases strongly at z>4. We show that this result is closely linked to the flattening in galaxy SSFRs at z>2 compared to halo specific mass accretion rates; we expect that average galaxy SSFRs at fixed stellar mass will continue their mild evolution to z~15. The expected CSFR shows no breaks or features at z>8.5; this constrains both reionization and the possibility of a steep falloff in the CSFR at z=9-10. Finally, we make predictions for stellar mass and luminosity functions for the James Webb Space Telescope (JWST), which should be able to observe one galaxy with M* > ~10^8 Msun per 10^3 Mpc^3 at z=9.6 and one such galaxy per 10^4 Mpc^3 at z=15.
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